JAZZ CLAUDIA ACUNA at Mezzrow (Sept. 6,8 p.m. and 9:30 p.m.). Ms. Acuna's voice has a burly center and a remarkable flexibility. Raised in Chile and based in New York, she began her career focused on standard jazz repertoire, but her affinities have always roved widely. Today her songbook encompasses Chilean folk, aqueous original compositions, Afro-Cuban classics and modern jazz tunes by her contemporaries. Ms. Acuna appears here with two fellow Chilean jazz musicians: the pianist Pablo Vergara and the bassist Pablo Menares. 646-476-4346, mezzrow.com
STEVE KUHN TRIO at Birdland (Sept. 5-9,8:30 and 11 p.m.). Mr. Kuhn is a prodigious pianist whose talents reveal themselves gently. For over 50 years he has honed a sound that's bright and stark, especially in the upper register. His playing is pleasant and reassuring, but also distinctive: He's influenced in equal measure by Bill Evans and Red Garland. He appears here with his working trio, featuring the bassist Steve Swallow and the drummer Joey Baron. The group will enter the studio to record its third album soon after this run of shows ends. 212-581-3080, birdlancljazz.com
GRASSELLA OLIPHANT at Dizzy's Club Coca-Cola (Sept. 1,7:30 p.m.). A drummer with a light but declarative touch, Mr. Oliphant played early in his career with the vocalists Sarah Vaughan and Gloria Lynne, as well as the pianist Ahmad Jamal. He released two soul-jazz albums as a leader in the 1960s, "The Grass Roots" and "The Grass Is Greener," both on Atlantic Records, but never became a household name. He eventually left the music business, staying away for decades before starting to perform publicly again in the new millennium. This concert at Dizzy's takes place on his 88th birthday, and features Freddie Hendrix on trumpet, Bruce Williams on alto saxophone, Lance Bryant on tenor saxophone, Brandon McCune on piano and Chris Berger on bass. It's the first show of the club's monthlong Coca-Cola Generations in Jazz Festival. 212-258-9595, jazz.org/dizzys
PAA KOW at Club Bonafide (Sept. 7, 7:30 and 9:30 p.m.). Raised in Ghana and now a world-traveling drummer based in Colorado, Paa Kow makes music that draws on various brands of free-flowing musical uplift: Ghanaian high life, American jam-band music and funk. He performs here with a nine-piece band to celebrate the coming release of a warmblooded third album, "Cookpot." 646-918-6189, clubbonafide.com
CRAIG TABORN at the Stone (Sept. 5-10, 8:30 p.m.). Mr. Taborn, a quietly untamable pianist, has released a slow but powerful stream of albums over the past few years: "Junk Magic," a prismatic, electric-acoustic patchwork; the stoic and minimalist solo piano record "Avenging Angel"; the trio album "Chants," full of dance-like beats and trellised interplay; and, this year, "Daylight Ghosts," a luminous, almost quiescent recording with a quartet. At the Stone next week, performing with a different project each night, he will have the chance to engage with something like the full breadth of his affinities. On Thursday Mr. Taborn plays with the "Daylight Ghosts" ensemble; on Sept. 9 he and the tenor saxophonist Chris Potter will helm a quintet; and on Sept. 10 he will perform a solo set. thestonenyc.com
JEFF (TAIN) WATTS at Jazz Standard (Sept. 5-10,7:30 and 9:30 p.m.). Mr. Watts, 57, known in the jazz world as Tain, might be the most important straight-ahead jazz drummer of his generation. Since the early 1980s, when he worked as a sideman for Wynton and Branford Marsalis, he's poured together the influences of the two great polyrhythmic instigators of the 1960s ? Tony Williams and Elvin Jones ? coming up with something newly combustive, and nearly as original. Here Mr. Watts pays tribute to one of those progenitors, gathering musicians who once played in Mr. Jones's band. They include the trumpeter Nicholas Payton, the trombonist Robin Eubanks and the pianist Eric Lewis.